Biomedical science careers-conversion course?!

I wasnt sure where to put this so I hope this is the right place!

Basically I had an interview today for a medical lab assistant job at the NHS, it went well so I hope I get the job

Im a graduate with a BSc, in the interview the woman asked me why wasnt I considering a more higher level job, for example biomedical science??

Now, I understand that to be a biomedical scientist you need a biomedical science degree, but are there any other jobs available which are a bit higher up than the lab assistant jobs, or are there conversion courses available for those who already have a BSc??

Ive looked on the NHS website and cant find anything and also the IBMS website, but I cant find anything!

Rep for any info, thanks!